Calibration apparatus, calibration curve creation method, and independent component analysis method

ABSTRACT

A calibration data acquisition unit (a) acquires Q optical spectra and S evaluation spectra, (b) extracts R subsets from a set of the Q optical spectra, (c) performs independent component analysis in which component amounts in each sample treated as independent components on each of R subsets so as to acquire R×N component calibration spectra, (d) obtains an inner product value between the R×N component calibration spectrum and an evaluation spectrum, (e) selects a component calibration spectrum for which a correlation degree between a component amount for the target component and the inner product value is the maximum as the target component calibration spectrum from among the R×N component calibration spectra, and (f) creates a calibration curve by using the target component calibration spectrum.

BACKGROUND 1. Technical Field

The present invention relates to a calibration technique of obtaining acomponent amount of a target component from measured data of a testobject, and an independent component analysis technique of determiningan independent component on the basis of measured data such as anoptical spectrum.

2. Related Art

In the related art, there is a calibration method of obtaining acomponent amount of a target component by using independent componentanalysis (ICA). The independent component analysis of the related art isa method of estimating signal sources as independent components on thepremise that the signal sources (for example, an optical spectra)derived from a plurality of components are independent components. Forexample, JP-A-2013-36973 discloses a calibration technique in which anoptical spectrum is acquired by performing spectrometry on a greenvegetable, a spectrum derived from chlorophyll is estimated as anindependent component by performing independent component analysis onthe optical spectrum, and a chlorophyll amount in a new green vegetablesample is determined by using the estimated spectrum.

Meanwhile, in order to sufficiently accurately perform independentcomponent analysis, the condition that a plurality of independentcomponents to be estimated are statistically independent from each otheris required to be established. However, in a certain kind of measureddata, such a condition for performing accurate independent componentanalysis may not be established.

In this case, there is a probability that optical spectra cannot beaccurately estimated even if normal independent component analysis inwhich optical spectra derived from a plurality of components are treatedas independent components is performed. Therefore, a technique ofperforming independent component analysis with high accuracy or atechnique of calibrating a target component with high accuracy isdesirable even in a case where the condition that optical spectraderived from a plurality of components are “statistically independentfrom each other” is not satisfied. This problem is not limited tocalibration of a target component using an optical spectrum including anear-infrared region, and is common to other techniques of performingindependent component analysis on other measured data or measuredsignals.

SUMMARY

An advantage of some aspects of the invention is to solve at least apart of the problems described above, and the invention can beimplemented as the following forms or application examples.

(1) According to a first aspect of the invention, a calibrationapparatus obtaining a component amount for a target component in a testobject is provided. The calibration apparatus includes an opticalspectrum acquisition unit that acquires an optical spectrum obtainedthrough spectrometry on the test object; a calibration data acquisitionunit that acquires calibration data including a target componentcalibration spectrum corresponding to the target component, and a singleregression formula indicating a calibration curve; an inner productvalue calculation unit that computes an inner product value between theoptical spectrum acquired for the test object and the target componentcalibration spectrum; and a component amount calculation unit thatcalculates a component amount for the target component corresponding toan inner product value obtained by the inner product value calculationunit by using the single regression formula indicating a relationshipbetween the inner product value and a component amount for the targetcomponent. The calibration data acquisition unit performs (a) a processof acquiring Q optical spectra obtained through spectrometry on Q (whereQ is an integer of 3 or more) first samples each containing N (where Nis an integer of 1 or more) components including the target component, Sevaluation spectra obtained through spectrometry on S (where S is aninteger of 3 or more) second samples in which a component amount for thetarget component is known; (b) a process of extracting R (where R is aninteger of 2 or more) subsets from a set of the Q optical spectra; (c) aprocess of determining N component calibration spectra corresponding tothe N components by performing independent component analysis in whichcomponent amounts for the N components are treated as independentcomponents in each sample on each of the R subsets, and acquiring atotal of R×N component calibration spectra; (d) a process of obtaining Sinner product values by performing an inner product between each of theR×N component calibration spectra and the S evaluation spectra; (e) aprocess of obtaining a correlation degree between a component amount forthe target component in the S second samples and the S inner productvalues with respect to each of the R×N component calibration spectra,and, from among the R×N component calibration spectra, selecting acomponent calibration spectrum causing the correlation degree to be themaximum as the target component calibration spectrum; and (f) a processof creating, as the calibration curve, a single regression formulaindicating a relationship between an inner product value obtainedthrough an inner product between the S evaluation spectra and the targetcomponent calibration spectrum, and a component amount for the targetcomponent contained in the S second samples.

According to the calibration apparatus, since independent componentanalysis in which component amounts for N components in each sample aretreated as independent components is performed, the independentcomponent analysis can be performed with high accuracy, and thuscalibration of a target component can be performed with high accuracy,even in a case where optical spectra derived from a plurality ofcomponents are not independent from each other. Since plurality ofsubsets are extracted from a set of Q optical spectra, and independentcomponent analysis in which a component amount is treated as anindependent component is performed on each of the subsets, even in acase where a component amount distribution in the whole set of the Qoptical spectra is a Gaussian distribution, and thus there is a subsetin which independency is deficient, independency is improved since acomponent amount distribution is a more non-Gaussian distribution inseveral subsets, and thus it is possible to obtain a target componentcalibration spectrum with high accuracy. As a result, it is possible toperform calibration with higher accuracy.

(2) In the process (c), the calibration data acquisition unit may (1)use an equation X=YW in which an optical spectrum matrix X havingoptical spectra obtained through spectrometry on each sample as columnvectors is the same as a product between a component natural spectrummatrix Y having unknown component natural spectra derived from therespective components among the N components contained in each of thesamples as column vectors and a component amount matrix W having unknowncomponent amounts for the N components in each of the samples as columnvectors, and perform independent component analysis in which therespective column vectors forming the component amount matrix W aretreated as independent components, so as to determine the componentamount matrix W and the component natural spectrum matrix Y, and (2)employ inverse matrix row vectors respectively corresponding to the Ncomponents in a general inverse matrix Y^(†) of the component naturalspectrum matrix Y determined through the independent component analysis,as the component calibration spectra corresponding to the respectivecomponents.

According to this configuration, it is possible to determine a componentcalibration spectrum corresponding to each component with high accuracy.

(3) According to a second aspect of the invention, a calibration curvecreation method performed by the calibration data acquisition unit inthe first aspect is provided.

According to the calibration method, in the same manner as in the firstaspect, it is possible to obtain target component calibration spectrumwith high accuracy, and to perform calibration with high accuracy.

(4) According to a third aspect of the invention, an independentcomponent analysis method in which component calibration spectracorresponding to a plurality of components contained in each sample aredetermined on the basis of a plurality of optical spectra obtainedthrough spectrometry on a plurality of samples is provided. Theindependent component analysis method includes (1) extracting aplurality of subsets each including two or more optical spectra from aset of optical spectra obtained through spectrometry on the plurality ofsamples; and (2) determining a plurality of component calibrationspectra respectively corresponding to the plurality of components byperforming independent component analysis in which component amounts forthe plurality of components in each sample are treated as independentcomponents on each of the plurality of subsets.

Since plurality of subsets are extracted from a set of a plurality ofoptical spectra, and independent component analysis in which a componentamount is treated as an independent component is performed on each ofthe subsets, even in a case where a component amount distribution in thewhole set of the plurality of optical spectra is a Gaussiandistribution, and thus there is a subset in which independency isdeficient, independency is improved since a component amountdistribution is a more non-Gaussian distribution in several subsets, andthus it is possible to obtain a target component calibration spectrumwith high accuracy.

The invention may be realized in aspects such as an electronic apparatusincluding the above-described apparatus, a computer program forrealizing functions of the respective units of the apparatus, and anon-transitory storage medium which stores the computer program thereon.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention will be described with reference to the accompanyingdrawings, wherein like numbers reference like elements.

FIG. 1 is a diagram illustrating an overview of independent componentanalysis in which component amounts are treated as independentcomponents.

FIG. 2 is a diagram illustrating an overview of a calibration curvecreation process using independent component analysis.

FIG. 3 is a diagram illustrating an overview of a target componentcalibration process.

FIG. 4 is a block diagram illustrating a configuration of a calibrationapparatus in an embodiment.

FIG. 5 is a flowchart illustrating procedures of a calibration process.

FIG. 6 is a flowchart illustrating a calibration data acquisitionprocess.

FIG. 7 is a diagram illustrating the content of the calibration dataacquisition process.

FIG. 8 is a graph illustrating a concentration distribution ofcomponents in all samples.

FIG. 9 is a graph illustrating calibration accuracy in a comparativeexample using all samples.

FIG. 10 is a graph illustrating a relationship between calibrationaccuracy and a correlation coefficient in an Example.

FIG. 11 is a graph illustrating a concentration distribution ofcomponents in an optimal subset in the Example.

FIG. 12 is a graph illustrating calibration accuracy obtained with anoptimal subset in the Example.

DESCRIPTION OF EXEMPLARY EMBODIMENTS

Hereinafter, an embodiment of the invention will be described in thefollowing order.

A. Overview of independent component analysis in which component amountsare treated as independent components

B. Overview of calibration curve creation process and calibrationprocess

C. Configuration of calibration apparatus and process content thereof inembodiment

D. Content of calibration data acquisition process

E. Example

F. Modification examples

A. OVERVIEW OF INDEPENDENT COMPONENT ANALYSIS IN WHICH COMPONENT AMOUNTSARE TREATED AS INDEPENDENT COMPONENTS

Independent component analysis used in an embodiment described below isgreatly different from typical independent component analysis in whichcomponent-derived measured data (for example, an optical spectrum) istreated as an independent component in that a component amount for acomponent is treated as an independent component. Therefore, first, adescription will be made of a difference between the typical independentcomponent analysis and the independent component analysis in which acomponent amount is treated as an independent component. Hereinafter,for convenience of description, a description will be made of a case ofusing an optical spectrum of a test object (also referred to as a“sample”) as measured data, but the independent component analysis inwhich a component amount is treated as an independent component isapplicable to different kinds of signals or data such as a sound signalor an image.

In the typical independent component analysis, for example, opticalspectra x₁(λ), x₂(λ), and x₃(λ) obtained through spectrometry on aplurality of samples are expressed as in the following Equation (1) as alinear combination of component natural spectra s₁(λ), s₂(λ), and s₃(λ)derived from a plurality of components contained in each sample.

$\begin{matrix}\begin{matrix}{{x_{1}(\lambda)} = {{a_{11}{s_{1}(\lambda)}} + {a_{12}{s_{2}(\lambda)}} + {a_{13}{s_{3}(\lambda)}}}} \\{{x_{2}(\lambda)} = {{a_{21}{s_{1}(\lambda)}} + {a_{22}{s_{2}(\lambda)}} + {a_{23}{s_{3}(\lambda)}}}} \\{{x_{3}(\lambda)} = {{a_{31}{s_{1}(\lambda)}} + {a_{32}{s_{2}(\lambda)}} + {a_{33}{s_{3}(\lambda)}}}}\end{matrix} & (1)\end{matrix}$

Here, a₁₁, a₁₂, . . . , and a₃₃ are weighting factors indicatingcomponent amounts for the respective components. Herein, for convenienceof description, the number of samples and the number of components inoptical spectra are assumed to be all three.

The above Equation (1) is expressed as in the following Equation (2) interms of a matrix.

$\begin{matrix}\begin{matrix}{\begin{bmatrix}{x_{1}(\lambda)} \\{x_{2}(\lambda)} \\{x_{3}(\lambda)}\end{bmatrix} = {A\begin{bmatrix}{s_{1}(\lambda)} \\{s_{2}(\lambda)} \\{s_{3}(\lambda)}\end{bmatrix}}} \\{A = \begin{bmatrix}a_{11} & a_{12} & a_{13} \\a_{21} & a_{22} & a_{23} \\a_{31} & a_{32} & a_{33}\end{bmatrix}}\end{matrix} & (2)\end{matrix}$

In the typical independent component analysis, unknown component naturalspectra s₁(λ), s₂(λ), and s₃(λ) derived from a plurality of componentsare treated as components which are independent from each other, and aresubjected to independent component analysis by using the above Equation(2). In this case, in order to sufficiently accurately performindependent component analysis, the condition that a plurality ofcomponent natural spectra s₁ (λ) , s₂ (λ) , and s₃ (λ) are statisticallyindependent from each other is required to be established.

However, the condition for performing accurate independent componentanalysis may not be established depending on property of measured data.In this case, optical spectra derived from a plurality of components maynot satisfy the condition of being “statistically independent from eachother”. In this case, even if the typical independent component analysisis performed by using the above Equation (2), the component naturalspectra s₁(λ), s₂(λ), and s₃(λ) or the component amount matrix A cannotbe accurately estimated.

The present inventor of the invention has found that the componentnatural spectra s₁(λ), s₂(λ), and s₃(λ) or the component amount matrix Acan be accurately estimated or determined by employing the independentcomponent analysis in which a component amount is treated as anindependent component instead of the above-described typical independentcomponent analysis.

In the independent component analysis in which a component amount istreated as an independent component, the following equation is usedinstead of the above Equation (2).

$\begin{matrix}\begin{matrix}\begin{bmatrix}{x_{1}(\lambda)}^{T} & {x_{2}(\lambda)}^{T} & {x_{3}(\lambda)}^{T}\end{bmatrix} & = & {\begin{bmatrix}{s_{1}(\lambda)}^{T} & {s_{2}(\lambda)}^{T} & {s_{3}(\lambda)}^{T}\end{bmatrix}\mspace{14mu} A^{T}} \\{A^{T} = \begin{bmatrix}a_{11} & a_{21} & a_{31} \\a_{12} & a_{22} & a_{32} \\a_{13} & a_{23} & a_{33}\end{bmatrix}} & \; & \;\end{matrix} & (3)\end{matrix}$

Here, the superscript “T” added to the matrix symbol indicates atransposed matrix. Equation (3) is obtained by transposing both of thesides in the above Equation (2).

In the independent component analysis in which a component amount istreated as an independent component, in the above Equation (3), thecolumn vectors [a₁₁ a₁₂ a₁₃]^(T), [a₂₁ a₂₂ a₂₃]^(T), and [a₃₁ a₃₂ a₃₃]^(T) of the component amount matrix A^(T) are respectively treated asindependent components, and independent component analysis is performed.These column vectors indicate component amounts for a plurality ofcomponents in each sample.

The independent component analysis in which a component amount istreated as an independent component is an analysis method employedthrough the following examination. As described above, there is a casewhere component natural spectra derived from a plurality of componentsdo not satisfy the condition of being statistically independent fromeach other. However, although component natural spectra derived from aplurality of components are not statistically independent from eachother, if the condition that component amounts (for example,concentrations) for the plurality of components have no relation to eachother and are statistically independent from each other is established,in a case where component amounts (that is, the respective columnvectors forming the component amount matrix A^(T) in the above Equation(3)) for a plurality of components in each sample are treated asindependent components, and independent component analysis is performed,it is possible to accurately estimate or determine the component amountmatrix A^(T), and also to accurately estimate or determine the componentnatural spectra s₁(λ), s₂(λ), and s₃(λ).

If the above Equation (3) is generalized, the following Equation (4) isobtained.

$\begin{matrix}\begin{matrix}{X^{T} = {S^{T}A^{T}}} \\{X^{T} = \begin{bmatrix}{x_{1}\left( \lambda_{1} \right)} & \ldots & {x_{M}\left( \lambda_{1} \right)} \\\vdots & \ddots & \vdots \\{x_{1}\left( \lambda_{K} \right)} & \ldots & {x_{M}\left( \lambda_{K} \right)}\end{bmatrix}} \\{S^{T} = \begin{bmatrix}{s_{1}\left( \lambda_{1} \right)} & \ldots & {s_{N}\left( \lambda_{1} \right)} \\\vdots & \ddots & \vdots \\{s_{1}\left( \lambda_{K} \right)} & \ldots & {s_{N}\left( \lambda_{K} \right)}\end{bmatrix}} \\{A^{T} = \begin{bmatrix}a_{11} & \ldots & a_{M\; 1} \\\vdots & \ddots & \vdots \\a_{1N} & \ldots & a_{MN}\end{bmatrix}}\end{matrix} & (4)\end{matrix}$

Here, K indicates the number of measurement points of the wavelength λin a spectrum, M indicates the number of samples, and N indicates thenumber of components. A component amount a_(mn) (where m is 1 to M, andn is 1 to N) is a component amount (for example, a concentration) for ann-th component in an m-th sample.

Since it is inconvenient to use matrices X^(T), S^(T), and A^(T) as inthe above Equation (4) with the transposition symbol, X=X^(T), Y=S^(T),y_(n)(λ_(k))=s_(n)(λ_(k)), W=A^(T), and w_(mn)=a_(mn) are set, and theabove Equation (4) is rewritten into the following Equation (5) which isused in independent component analysis in which a component amount istreated as an independent component.

Equations used in independent component analysis in which componentamount is treated as independent component

$\begin{matrix}\begin{matrix}{X = {YW}} \\{X = \begin{bmatrix}{x_{1}\left( \lambda_{1} \right)} & \ldots & {x_{M}\left( \lambda_{1} \right)} \\\vdots & \ddots & \vdots \\{x_{1}\left( \lambda_{K} \right)} & \ldots & {x_{M}\left( \lambda_{K} \right)}\end{bmatrix}} \\{Y = \begin{bmatrix}{y_{1}\left( \lambda_{1} \right)} & \ldots & {y_{N}\left( \lambda_{1} \right)} \\\vdots & \ddots & \vdots \\{y_{1}\left( \lambda_{K} \right)} & \ldots & {y_{N}\left( \lambda_{K} \right)}\end{bmatrix}} \\{W = \begin{bmatrix}w_{11} & \ldots & w_{M\; 1} \\\vdots & \ddots & \vdots \\w_{1N} & \ldots & w_{MN}\end{bmatrix}}\end{matrix} & (5)\end{matrix}$

Here, x_(m)(λ_(k)) indicates a spectral intensity at a wavelength λ_(k)in an m-th sample, y_(n)(λ_(k)) indicates a spectral intensity at thewavelength λ_(k) derived from an n-th component, and w_(mn) indicates acomponent amount for the n-th component in the m-th sample. K indicatesthe number of measurement points of the wavelength λ in a spectrum, Mindicates the number of samples, and N indicates the number ofcomponents. K and M are all integers of 2 or more. N is an integer of 1or more, and may be an integer of 2 or more.

The above Equation (5) corresponds to an equation in which an opticalspectrum matrix X having optical spectra obtained through spectrometryon each sample as column vectors [x_(m)(λ₁) . . . x_(m)(λ_(K))]^(T) isthe same as a product between a component natural spectrum matrix Yhaving unknown component natural spectra derived from a plurality ofrespective components as column vectors [y_(n)(λ₁) . . .y_(n)(λ_(K))]^(T) and a component amount matrix W having unknowncomponent amounts indicating component amounts for a plurality ofcomponents in each sample as column vectors [w_(m1) . . . w_(mN)]^(T).

FIG. 1 is a diagram illustrating an overview of independent componentanalysis in which a component amount is treated as an independentcomponent. FIG. 1 illustrates an example of a case where an aqueoussolution containing glucose or albumin is used as a sample, and opticalspectra obtained through spectrometry on a plurality of samples are usedas independent component analysis objects. A measured spectrum Xd is anabsorbance spectrum obtained through spectrometry. A plurality of actualmeasured spectra Xd show considerably approximate curves, but, in FIG.1, for convenience of illustration, differences among the plurality ofmeasured spectra Xd are illustrated to be exaggerated. The measuredspectra Xd for a plurality of samples have values approximate to eachother, and, thus, if these values are used as they are, there is aprobability that the accuracy of a result obtained through independentcomponent analysis may not be sufficiently high. For example, theinfluence of a solvent on a measured spectrum may change depending onthe concentration of a solute (contained component), and thus theaccuracy of independent component analysis may deteriorate. Therefore,as preprocessing, a subtraction calculation is performed so that anaverage spectrum Xave of a plurality of measured spectra Xd issubtracted from each measured spectrum Xd, and thus a differencespectrum X is obtained. In the above-described way, even in a case wherethe influence of a solvent on a measured spectrum changes depending onthe concentration of a solute (contained component), the influence canbe removed through the preprocessing, and thus it is possible toincrease the accuracy of independent component analysis. The differencespectrum X is used as the optical spectrum X in the above Equation (5).If independent component analysis is performed on the differencespectrum X, the accuracy of the independent component analysis can beimproved. However, preprocessing may be omitted.

The lower part in FIG. 1 illustrates a state in which the opticalspectrum X is expressed by a product between the unknown componentnatural spectrum y_(n)(λ) and the unknown component amount w_(mn),according to the above Equation (5).

In the independent component analysis, the component amount matrix W isdetermined by treating each column vector [w_(m1) . . . w_(mN)]^(T) ofthe component amount matrix W in the above Equation (5) as anindependent component and performing the independent component analysis,and, as a result, the component natural spectrum matrix Y is alsodetermined. An independent component analysis method may employ thetypical independent component analysis. For example, an independentcomponent analysis method disclosed in JP-A-2013-160574 orJP-A-2016-65803 filed by the applicant of the present application may beused, or other independent component analysis methods may be used.

If the component natural spectrum matrix Y in the above Equation (5) isdetermined, a component amount w* for a plurality of components in a newsample may be obtained by integrating an optical spectrum x* obtainedthrough spectrometry on the new sample with a general inverse matrixY^(†) of the component natural spectrum matrix Y obtained through theindependent component analysis. Specifically, the component amount w*for the components of the new sample may be obtained by using thefollowing Equation (6).

$\begin{matrix}\begin{matrix}{w^{*} = {Y^{\dagger}x^{*}}} \\{w^{*} = \begin{bmatrix}w_{1}^{*} \\\vdots \\w_{N}^{*}\end{bmatrix}} \\{Y^{\dagger} = \begin{bmatrix}{y_{1}^{\ddagger}\left( \lambda_{1} \right)} & \ldots & {y_{1}^{\ddagger}\left( \lambda_{K} \right)} \\\vdots & \ddots & \vdots \\{y_{N}^{\ddagger}\left( \lambda_{1} \right)} & \ldots & {y_{N}^{\ddagger}\left( \lambda_{K} \right)}\end{bmatrix}} \\{x^{*} = \begin{bmatrix}{x^{*}\left( \lambda_{1} \right)} \\\vdots \\{w^{*}\left( \lambda_{K} \right)}\end{bmatrix}}\end{matrix} & (6)\end{matrix}$

Here, w*=[w₁* . . . w_(N)*]^(T) is a component amount for N componentsincluded in a new sample, Y^(†) is a general inverse matrix of thecomponent natural spectrum matrix Y obtained through independentcomponent analysis, y_(n)(λ_(k))^(‡) is a k-th element of a row vectorof an n-th row in the general inverse matrix Y^(†), and x*=[x*(λ₁) . . .x*(λ_(K))]^(T) is an optical spectrum obtained through spectrometry onthe new sample. The above Equation (6) may be derived by multiplying thelefts of both sides in the above Equation (5) by the general inversematrix Y^(†) of the component natural spectrum matrix Y.

A value of a component amount w_(n)* for any n-th component of the newsample is obtained according to the following Equation (7) derived fromthe above Equation (6).

w _(n) *=y _(n) ^(‡) x*

y _(n) ^(‡) =[y _(n) ^(‡)(λ₁) . . . y _(n) ^(‡)(λ_(K))]  (7)

Here, y_(n) ^(‡) is a row vector of an n-th row in the general inversematrix Y^(†) of the component natural spectrum matrix Y. The row vectory_(n) ^(‡) is also referred to as an “inverse matrix row vector y_(n)^(‡)” or a “component calibration spectrum y_(n) ^(‡)”. The generalinverse matrix Y^(†) of the component natural spectrum matrix Y isreferred to as a “component calibration spectrum matrix Y^(†)”. Asmentioned above, the general inverse matrix Y^(†) may be obtained on thebasis of the component natural spectrum matrix Y obtained throughindependent component analysis, and the component amount w_(n)* for then-th component may be obtained by taking an inner product between theinverse matrix row vector y_(n) ^(‡) (that is, the n-th componentcalibration spectrum y_(n) ^(†)) corresponding to the n-th component inthe general inverse matrix Y^(†) and the optical spectrum x* for the newsample. However, the component natural spectrum matrix Y obtainedthrough independent component analysis is meaningless in a value of anelement thereof, and has property in which a waveform thereof isproportional to a true component natural spectrum. Therefore, thecomponent amount w_(n)* obtained through the inner product in the aboveEquation (7) is a value which is proportional to an actual componentamount. An actual component amount may be obtained by applying the innerproduct value w_(n)* obtained through the inner product in the aboveEquation (7) to a calibration curve (described later).

As mentioned above, according to the independent component analysis inwhich a component amount is treated as an independent component, even ina case where component natural spectra derived from a plurality ofcomponents are not statistically independent from each other, thecomponent amount matrix W and the component natural spectrum matrix Y(and the component calibration spectrum matrix Y^(†) which is a generalinverse matrix) can be accurately estimated or determined.

B. OVERVIEW OF CALIBRATION CURVE CREATION PROCESS AND CALIBRATIONPROCESS

FIG. 2 is a diagram illustrating an overview of a component analysis(ICA) in which a component amount is treated as an independentcomponent. An upper left part in FIG. 2 illustrates examples of measuredspectra MS obtained through spectrometry on a plurality of samples. Themeasured spectra MS correspond to the measured spectra Xd in FIG. 1, andmay be obtained through spectrometry on a sample containing a pluralityof components (for example, glucose and albumin). In atypicalcalibration curve creation process, as a plurality of samples, knownsamples in which a component amount (for example, a concentration) for atarget component (for example, glucose) is known are used. However, inan embodiment which will be described later, there is a difference fromthe typical calibration curve creation process in that samples (firstsamples) in which a component amount for a target component is unknownmay be used as a plurality of samples for acquiring optical spectra asindependent component analysis objects.

In creation of a calibration curve, first, preprocessing is performed onthe measured spectra MS, and thus optical spectra OS (the opticalspectra X having undergone preprocessing in FIG. 1) having undergone thepreprocessing are created. As the preprocessing, for example,preprocessing including normalization of the measured spectra MS isperformed. In the preprocessing, a subtraction calculation described inFIG. 1 is also preferably performed in addition to normalization. In thepreprocessing, project on null space (PNS) may be performed in order toremove a baseline variation in the measured spectra MS. However, in acase where initial measured spectra MS have characteristics of notrequiring preprocessing (for example, in a case where the measuredspectra MS do not vary due to normalization), preprocessing may beomitted, and the measured spectra MS may be used as the optical spectraOS without being changed.

Next, independent component analysis in which a component amount istreated as an independent component is performed on a plurality ofoptical spectra OS, and thus a plurality of component calibrationspectra CS₁ to CS_(N) are obtained. The number in the parenthesisindicates a component number. The plurality of component calibrationspectra CS₁ to CS_(N) correspond to the above-described componentcalibration spectra y_(n) ^(‡).

A lower part in FIG. 2 illustrates a method of creating a calibrationcurve by using the plurality of component calibration spectra CS₁ toCS_(N) obtained in the above-described way. Herein, first, opticalspectra EDS regarding a plurality of known samples (second samples) inwhich a component amount for a target component is known are acquired.The optical spectra EDS are obtained by performing, as necessary, theabove-described preprocessing on measured spectra which are obtainedthrough spectrometry on the known samples. The optical spectra EDS arereferred to as “evaluation spectra EDS”. Next, an inner product valuebetween the individual evaluation spectra EDS and the componentcalibration spectrum CS_(n) is computed. The computation of the innerproduct value is a calculation in which each of the evaluation spectraEDS and the component calibration spectrum CS_(n) are treated as asingle vector, and an inner product between the two vectors is taken,and, as a result, a single inner product value is obtained. Therefore,if inner products between the same component calibration spectrum CS_(n)and a plurality of evaluation spectra EDS are computed, a plurality ofinner product values corresponding to a plurality of known samples areobtained with respect to the same component calibration spectrum CS_(n).A lower right part in FIG. 2 shows diagrams in which inner productvalues P regarding a plurality of known samples are taken on atransverse axis, a known component amount C for a target componentcontained in the plurality of known samples is taken on a longitudinalaxis, and the values are plotted. If the n-th component calibrationspectrum CS_(n) used for an inner product is a spectrum corresponding toa target component, as in the example illustrated in FIG. 2, the innerproduct value P and the component amount C for the target component ofeach known sample have a strong correlation. Therefore, from among theplurality of component calibration spectra CS₁ to CS_(N) obtainedthrough the independent component analysis, the component calibrationspectrum CS_(n) having the strongest correlation (the greatestcorrelation degree) may be selected as a target component calibrationspectrum corresponding to the target component. As an evaluation valuefor such selection, evaluation values other than the correlation degreemay be used. In the example illustrated in FIG. 2, the first componentcalibration spectrum CS₁ is a target component calibration spectrumcorresponding to the target component (for example, glucose). Acalibration curve CC is represented as a straight line given by a singleregression formula C=uP+v for plotting the inner product value P and thecomponent amount C.

FIG. 3 is a diagram illustrating an overview of a target componentcalibration process using a calibration curve. The calibration processis performed by using the target component calibration spectrum CS₁ andthe calibration curve CC obtained through the calibration curve creationprocess illustrated in FIG. 2. In the calibration process, first, ameasure spectrum TOS of a test object in which a component amount for atarget component is unknown is acquired. Next, preprocessing isperformed on the measure spectrum TOS as necessary, and thus an opticalspectrum TOS having undergone the preprocessing is created. Thispreprocessing is the same processing as the preprocessing used forcreation of the calibration curve. In the preprocessing during creationof the calibration curve, in a case where a subtraction calculationdescribed in FIG. 1 is performed, the average spectrum Xave used duringcreation of the calibration curve may be subtracted from the measurespectrum TOS. An inner product between the optical spectrum TOS obtainedin the above-described way and the target component calibration spectrumCS₁ is taken, and thus an inner product value P regarding the opticalspectrum TOS is calculated. If the inner product value P is applied tothe calibration curve CC, a component amount C for the target componentcontained in the test object can be determined.

C. CONFIGURATION OF CALIBRATION APPARATUS AND PROCESS CONTENT THEREOF INEMBODIMENT

FIG. 4 is a block diagram illustrating a configuration of a calibrationapparatus 100 in an embodiment. The calibration apparatus 100 includes acalibration data acquisition unit 110, an optical spectrum acquisitionunit 120, an inner product value calculation unit 130, a componentamount calculation unit 140, and a display unit 150. A measurementdevice 200 for acquiring measured data is connected to the calibrationapparatus 100. The measurement device 200 is, for example, aspectrometer measuring spectral absorbance of a sample. The measurementdevice 200 is not limited to a spectrometer, and various measurementdevices suitable for characteristics of target components can be used.

The calibration apparatus 100 maybe implemented by, for example, anelectronic apparatus for use in calibration only, and may be implementedby a general purpose computer. Functions of the respective units 110 to150 of the calibration apparatus 100 may be implemented by any computerprograms or hardware circuits.

FIG. 5 is a flowchart illustrating procedures of a calibration processperformed by the calibration apparatus 100. In step S110, thecalibration data acquisition unit 110 (FIG. 4) acquires calibration dataincluding a target component calibration spectrum (CS₁ in the exampleillustrated in FIG. 2) and the calibration curve CC. Details of thecalibration data acquisition process in the present embodiment will bedescribed later.

In step S120, the optical spectrum acquisition unit 120 acquires theoptical spectrum. TOS (FIG. 3) of a test object by using the measurementdevice 200. As described in FIG. 3, the optical spectrum TOS is obtainedby performing preprocessing on a measure spectrum obtained throughspectrometry, as necessary. Therefore, the optical spectrum acquisitionunit 120 preferably has a function of performing the preprocessing. Instep S130, the inner product value calculation unit 130 calculates theinner product value P (FIG. 3) between the optical spectrum TOS and thetarget component calibration spectrum CS₁. In step S140, the componentamount calculation unit 140 calculates the component amount Ccorresponding to the inner product value P obtained in step S130 byusing the calibration curve CC. The component amount C is a componentamount (for example, a glucose concentration) for the target componentin the test object. In step S150, the component amount C is displayed onthe display unit 150. Instead of the component amount C being displayed,the component amount C may be transmitted to another electronicapparatus, and other desired processes (for example, a notification sentto a test object using an electronic mail) may be performed.

D. CONTENT OF CALIBRATION DATA ACQUISITION PROCESS

FIGS. 6 and 7 are flowchart illustrating the calibration dataacquisition process in the present embodiment and diagrams illustratingthe content thereof, and illustrate detailed steps of step S110 in FIG.5.

In step S210, measurement is performed on Q (where Q is an integer of 3or more) first samples containing a plurality of components including atarget component (for example, glucose) so that a set of Q opticalspectra OS (FIG. 7) is acquired, and measurement is performed on S(where S is an integer of 3 or more) second samples in which a componentamount for the target component is known so that S pieces of evaluationdata ED (FIG. 7) are acquired. The set of the Q optical spectra OS islearning sample data for determining a component calibration spectrum byperforming independent component analysis. The evaluation data EDincludes the evaluation spectra EDS which are optical spectra for the Ssamples and a known component amount for the target component in eachsample. In the Q first samples, a component amount for the targetcomponent may be known, but samples in which a component amount for thetarget component is unknown may be used. This is because, in thecalibration data acquisition process of the present embodiment, acomponent amount of the target component in the Q first samples is notused. The number Q of first samples may be any integer of 3 or more,but, if Q is a great value of 100 or more, an effect achieved by theprocess in FIG. 6 is large. This is because, if the number Q of firstsamples increases, a component amount distribution is similar to aGaussian distribution, thus it is difficult to perform independentcomponent analysis in which a component amount is treated as anindependent component with high accuracy, and, as a result, it isnotably meaningful to create a subset which will be described later. Thereason will be supplementarily described below.

In order to perform the above-described independent component analysisin which a component amount is treated as an independent component withhigh accuracy, a plurality of pieces of sample data (optical spectra)are required, and a set of the sample data preferably satisfies thefollowing conditions.

Condition C1

A plurality of optical spectra are data obtained by performingmeasurement on a sample in which various components which can be presentduring actual measurement on a test object except for a specific targetcomponent are mixed with each other.

Condition C2

A component amount distribution of a plurality of components including atarget component are statistically independent from each other accordingto a non-Gaussian distribution.

The above condition C1 may be satisfied by performing measurement undervarious measurement conditions. However, the condition C2 is not ensuredto be satisfied in a set of sample data which is prepared at random.Particularly, with respect to data collected from a plurality ofdifferent samples, a component amount distribution may be similar to anormal distribution (Gaussian distribution). On the other hand, not withrespect to the whole set of samples but with respect to a subsetthereof, it is expected that a component amount distribution deviatedfrom a normal distribution can be obtained. Therefore, in the presentembodiment, in step S220 which will be described later, a subset isextracted from a set of optical spectra OS of all prepared samples, andthus independent component analysis in which a component amount istreated as an independent component is improved.

The number S of second samples in which a component amount is known maybe any integer of 3 or more, and a larger number S is preferable in thatcalibration accuracy is improved. Typically, the number S of secondsamples is smaller than the number Q of first samples. Some or all ofthe second samples may be used as parts of the first samples.

In step S220, R (where R is an integer of 2 or more) subsets PA₁ toPA_(R) (FIG. 7) are extracted from the set of the Q optical spectra OS.Each of the R subsets PA₁ to PA_(R) is extracted to include M (where Mis an integer of 2 or more and below Q) optical spectra OS. The number Mof optical spectra OS forming each subset PA_(r) (where r is 1 to R) isset to a value which is equal to or more than the number of componentcalibration spectra obtained through the independent component analysisperformed in step S230. The numbers M of optical spectra OS forming therespective subsets PA_(r) (where r is 1 to R) may be values which aredifferent from or the same as each other. Extraction of the subsets PA₁to PA_(R) is preferably performed at random by using random numbers. Inextraction of each subset PA_(r) (where r is 1 to R), sampling withoutreplacement is used so that the same optical spectrum is not extractedtwice or more in the same subset PA_(r). The number of combinations ofselecting M different optical spectra from among the Q optical spectraOS is the same as _(Q)C_(M). The number R of subsets PA_(r) may be setto be equal to or less than the number _(Q)C_(M) of combinations, or maybe set to any integer of 2 or more. As mentioned above, if the R subsetsPA₁ to PA_(R) are extracted from the Q optical spectra OS prepared instep S210, one or more subsets PA_(r) satisfying the above condition C2are expected to be generated.

In step S230, the above-described independent component analysis inwhich a component amount is treated as an independent component isperformed on each of the R subsets PA₁ to PA_(R) so that N componentcalibration spectra CS_(r1) to CS_(rN) are obtained with respect to eachsubset PA_(r) (where r is 1 to R) (FIG. 7). As a result, a total of R×Ncomponent calibration spectra CS_(rn) (where r is 1 to R, and n is 1 toN) can be acquired. The number N of components is not required to matchthe number of actually contained components, and is empirically orexperimentally determined so that the accuracy of independent componentanalysis is improved. A value of N may be set to an integer of 1 ormore, but may be an integer of 2 or more.

Steps S240 to S260 are processes of selecting an optimal targetcomponent calibration spectrum corresponding to the target componentfrom among the R×N component calibration spectra CS_(rn) (where r is 1to R, and n is 1 to N) obtained in step S230. First, in step S240, aninner product is performed between each of the R×N component calibrationspectra CS_(rn) and the S evaluation spectra EDS so that S inner productvalues P are obtained. In other words, the S inner product values P arecalculated for a single component calibration spectrum CS_(rn).

In step S250, a correlation degree CD_(rn) between the known componentamount C for the target component in the S second samples and the Sinner product values P calculated for the component calibration spectraCS_(rn) are obtained with respect to each of the R×N componentcalibration spectra CS_(rn). Graphs in which a relationship between theinner product value P and the component amount C of the target componentis plotted with respect to each of the component calibration spectraCS_(rn) are drawn on the right end in FIG. 7. As the correlation degreeCD_(rn), for example, a correlation coefficient may be used.

In step S260, from among the R×N component calibration spectra CS_(rn),a single component calibration spectrum CS_(rn) causing the correlationdegree CD_(rn) to be greatest is selected as a target componentcalibration spectrum corresponding to the target component. In theexample illustrated in FIG. 7, since the correlation degree CD₁₁ of thecomponent calibration spectrum CS₁₁ is greatest, the componentcalibration spectrum CS₁₁ is selected as a target component calibrationspectrum.

In step S270, the single regression formula C=uP+v (refer to FIG. 2)indicating a relationship between the S inner product values P obtainedthrough an inner product between the S evaluation spectra EDS and thetarget component calibration spectrum CS₁₁, and the known componentamount C for the target component in the S second samples is created asthe calibration curve CC by using the target component calibrationspectrum CS₁₁ selected in the above-described way. The S inner productvalues P regarding the target component calibration spectrum CS₁₁ arealready obtained in step S240, and thus the S inner product values P maybe used without being changed in step S270.

As mentioned above, in the present embodiment, since independentcomponent analysis in which component amounts for N components aretreated as independent components is performed, the independentcomponent analysis can be performed with high accuracy, and thuscalibration of a target component can be performed with high accuracy,even in a case where optical spectra derived from a plurality ofcomponents are not independent from each other. In the presentembodiment, a plurality of subsets PA_(r) are extracted from a set of Qoptical spectra OS, and independent component analysis in which acomponent amount is treated as an independent component is performed oneach of the subsets PA_(r). In the above-described way, even in a casewhere a component amount distribution in the whole set of the Q opticalspectra OS is a Gaussian distribution, and thus there is a subset inwhich independency is deficient, independency is improved since acomponent amount distribution is a more non-Gaussian distribution inseveral subsets PA_(r), and thus it is possible to obtain a targetcomponent calibration spectrum with high accuracy. As a result, it ispossible to perform calibration with higher accuracy.

E. EXAMPLE Creation of Sample

In an Example, an aqueous solution which is a mixture of glucose as atarget component, albumin as another component, and water was used as afirst sample and a second sample. Specifically, the first sample foracquiring the optical spectra OS is an aqueous solution in which theglucose and the albumin are respectively mixed with pure water inconcentration ranges of 50 to 400 mg/dL and 4000 to 5000 mg/dL. Here,component amounts (concentrations) of the glucose and the albumin wereset to concentrations determined as random values following a normaldistribution in which the set range is included in 3σ with the center ofthe set range as an average value. In other words, independent componentanalysis with high accuracy was expected not to be performed on theentire first sample. The number Q of first samples was 5000.

In the same manner as the first sample, the second sample for acquiringthe evaluation data ED is also an aqueous solution in which the glucoseand the albumin are respectively mixed with pure water in concentrationranges of 50 to 400 mg/dL and 4000 to 5000 mg/dL. However, the secondsample is an aqueous solution in which a true value of the glucoseconcentration is measured and is known through chemical analysis. In theExample, the number S of second samples was 10.

Acquisition of Optical Spectra OS or the Like (Step S210 in FIG. 6)

The optical spectra OS were acquired from the first samples according tothe procedures in FIGS. 6 and 7, and the evaluation data ED was acquiredfrom the second samples. First, spectrometry including a near-infraredwavelength region of 1100 to 1300 nm was performed on the 5000 firstsamples so that 5000 measure spectra were acquired, and preprocessingwas performed thereon so that the optical spectra OS were acquired.Similarly, the evaluation spectra EDS were acquired for the ten secondsamples in which the concentration of the glucose which is a targetcomponent is known.

Extraction of Subset (Step S220)

Next, 500 different optical spectra OS were selected from a set of the5000 optical spectra OS at random, and 10000 subsets PA_(r) werecreated. In other words, the number R of subsets PA_(r) was set to10000, and the number M of optical spectra OS forming each subset PA_(r)was set to 500. Here, the number of combinations of selecting 500 from5000 is ₅₀₀₀C₅₀₀=1.52×10⁷⁰⁴, and the 10000 subsets PA_(r) are extremelysmall parts thereof.

Independent Component Analysis on Subsets (Step S230)

Next, independent component analysis in which a component amount istreated as an independent component was performed on the 10000 subsetsPA_(r) so that three component calibration spectra CS_(rn) (where r is 1to 10000, and n is 1 to 3) corresponding to the three components wereobtained. In other words, 30000 component calibration spectra CS_(rn)were obtained as a whole.

Calculation of Inner Product Value (Step S240)

Inner products with the 10 evaluation spectra EDS were calculated withrespect to each of the component calibration spectra CS, so that teninner product values P were obtained.

Calculation of Correlation Degree and Selection of Target ComponentCalibration Spectrum (steps S250 and S260)

The correlation degree CD_(rn) (correlation coefficient) between theinner product value P and the component amount C was computed as anevaluation index of the component calibration spectra CS_(rn) on thebasis of the ten inner product values P regarding each of the componentcalibration spectra CS_(rn) and the known component amount C (glucoseconcentration) of the glucose of the second samples. The componentcalibration spectrum CS_(rn) for which the correlation degree CD_(rn)was the maximum was selected as an optimal target component calibrationspectrum corresponding to the glucose (target component).

Creation of Calibration Data (step S270)

The single regression formula C=uP+v indicating a relationship betweenthe ten inner product values P obtained through the inner productbetween the ten evaluation spectra EDS and the target componentcalibration spectrum, and the known component amount C for the targetcomponent in the ten second samples is created as a calibration curve byusing the selected target component calibration spectrum.

In a comparative example, the process (extraction of subsets) in stepS220 in FIG. 6 is not performed, independent component analysis in whicha component amount was treated as an independent component was performedon the whole set of 5000 optical spectra OS in step S230, and threecomponent calibration spectra CS were determined. The processes in stepS240 and the subsequent steps were performed in the same manner as inthe above-described Example.

FIG. 8 is a graph illustrating concentration distributions of glucoseand albumin for the 5000 first sample. FIG. 9 is a graph illustratingcalibration accuracy in the comparative example, in which a transverseaxis expresses a true value of a glucose concentration, and alongitudinal axis expresses a calibration value. In the comparativeexample, calibration accuracy SEP of the glucose concentration was 51.5mg/dL, and a correlation coefficient Corr between the calibration valueand the true value of the glucose concentration was 0.744. As can beunderstood from FIG. 9, distributions of the calibration value and thetrue value are greatly spread, and thus the calibration accuracy is low.

FIG. 10 is a graph illustrating a relationship between the calibrationaccuracy obtained for the 30000 component calibration spectra CS_(rn)obtained in the Example and a correlation coefficient between thecalibration value and the true value. According to this result, it canbe seen that, as a correlation coefficient between the calibration valueand the true value becomes larger, the calibration accuracy becomes morefavorable.

FIG. 11 is a graph illustrating concentration distributions of theglucose and the albumin with respect to 500 samples corresponding to theoptimal subsets PA_(r) in the Example. FIG. 12 is a graph illustratingcalibration accuracy obtained with the optimal subsets PA_(r) in theExample. In the Example, the calibration accuracy SEP of the glucoseconcentration was 0.58 mg/dL, the correlation coefficient Corr betweenthe calibration value and the true value of the glucose concentrationwas 1.000, and both of the two results were more favorable than in thecomparative example. Therefore, it was confirmed that the independentcomponent analysis could be performed with high accuracy, andcalibration of glucose as a target component could also be performedwith high accuracy, according to the embodiment of the embodiment.

F. MODIFICATION EXAMPLES

The invention is not limited to the above-described embodiment oralternations thereof, and can be implemented in various aspects withinthe scope without departing from the spirit of the invention and may bemodified as follows, for example.

Modification Example 1

In the above-described embodiment and Example, a description has beenmade of a case where an aqueous solution containing glucose is used as asample, but the invention is applicable to other samples. For example,the invention is applicable to a case where a liquid containing a saltor liquid containing a protein such as a lipid or albumin or an alcoholis used as a sample. The invention is also applicable to independentcomponent analysis in which other objects such as a human body (human),a voice, and an image are used as samples. In a case where a human bodyis an object, the invention is applicable to a case with neutral fat oralcohol in the human body, or glucose in blood as a target component. Ina case where data or a signal other than a spectrum is an independentcomponent analysis object, the word “spectrum” may be replaced withother words such as “measured data” or “object data”.

Modification Example 2

Regarding apparatuses to which the invention is applicable, theinvention is also applicable to an apparatus in which a componentconcentration is estimated on the basis of spectrometric data of anoptically mid-infrared spectroscopic type, near-infrared spectroscopictype, or Raman spectroscopic type. The invention is also applicable toany one of an optical protein concentration meter, an optical neutralfat concentration meter, an optical blood glucose meter, an optical saltconcentration meter, and an optical alcohol concentration meter.

The entire disclosure of Japanese Patent Application No. 2016-186728filed Sep. 26, 2016 is hereby incorporated herein by reference.

What is claimed is:
 1. A calibration apparatus which obtains a componentamount for a target component in a test object, comprising: an opticalspectrum acquisition unit that acquires an optical spectrum obtainedthrough spectrometry on the test object; a calibration data acquisitionunit that acquires calibration data including a target componentcalibration spectrum corresponding to the target component, and a singleregression formula indicating a calibration curve; an inner productvalue calculation unit that computes an inner product value between theoptical spectrum acquired for the test object and the target componentcalibration spectrum; and a component amount calculation unit thatcalculates a component amount for the target component corresponding toan inner product value obtained by the inner product value calculationunit by using the single regression formula indicating a relationshipbetween the inner product value and a component amount for the targetcomponent, wherein the calibration data acquisition unit performs (a) aprocess of acquiring Q optical spectra obtained through spectrometry onQ (where Q is an integer of 3 or more) first samples each containing N(where N is an integer of 1 or more) components including the targetcomponent, and S evaluation spectra obtained through spectrometry on S(where S is an integer of 3 or more) second samples in which a componentamount for the target component is known, (b) a process of extracting R(where R is an integer of 2 or more) subsets from a set of the Q opticalspectra, (c) a process of determining N component calibration spectracorresponding to the N components by performing independent componentanalysis in which component amounts for the N components are treated asindependent components in each sample on each of the R subsets, andacquiring a total of R×N component calibration spectra, (d) a process ofobtaining S inner product values by performing an inner product betweeneach of the R×N component calibration spectra and the S evaluationspectra, (e) a process of obtaining a correlation degree between acomponent amount for the target component in the S second samples andthe S inner product values with respect to each of the R×N componentcalibration spectra, and, from among the R×N component calibrationspectra, selecting a component calibration spectrum causing thecorrelation degree to be greatest as the target component calibrationspectrum, and (f) a process of creating, as the calibration curve, asingle regression formula indicating a relationship between an innerproduct value obtained through an inner product between the S evaluationspectra and the target component calibration spectrum, and a componentamount for the target component contained in the S second samples. 2.The calibration apparatus according to claim 1, wherein, in the process(c), the calibration data acquisition unit (1) uses an equation X=YW inwhich an optical spectrum matrix X having optical spectra obtainedthrough spectrometry on each sample as column vectors is the same as aproduct between a component natural spectrum matrix Y having unknowncomponent natural spectra derived from respective components among the Ncomponents contained in each of the samples as column vectors and acomponent amount matrix W having unknown component amounts for the Ncomponents in each of the samples as column vectors, and performsindependent component analysis in which the respective column vectorsforming the component amount matrix Ware treated as independentcomponents, so as to determine the component amount matrix W and thecomponent natural spectrum matrix Y, and (2) employs inverse matrix rowvectors respectively corresponding to the N components in a generalinverse matrix Y^(†) of the component natural spectrum matrix Ydetermined through the independent component analysis, as the componentcalibration spectra corresponding to the respective components.
 3. Acalibration curve creation method of creating a calibration curve usedto obtain a component amount for a target component contained in a testobject, the method comprising: (a) acquiring Q optical spectra obtainedthrough spectrometry on Q (where Q is an integer of 3 or more) firstsamples each containing N (where N is an integer of 1 or more)components including the target component, and S evaluation spectraobtained through spectrometry on S (where S is an integer of 3 or more)second samples in which a component amount for the target component isknown; (b) extracting R (where R is an integer of 2 or more) subsetsfrom a set of the Q optical spectra; (c) determining N componentcalibration spectra corresponding to the N components by performingindependent component analysis in which component amounts for the Ncomponents are treated as independent components in each sample on eachof the R subsets, and acquiring a total of R×N component calibrationspectra; (d) obtaining S inner product values by performing an innerproduct between each of the R×N component calibration spectra and the Sevaluation spectra; (e) obtaining a correlation degree between acomponent amount for the target component in the S second samples andthe S inner product values with respect to each of the R×N componentcalibration spectra, and, from among the R×N component calibrationspectra, selecting a component calibration spectrum causing thecorrelation degree to be greatest as a target component calibrationspectrum; and (f) creating, as the calibration curve, a singleregression formula indicating a relationship between an inner productvalue obtained through an inner product between the S evaluation spectraand the target component calibration spectrum, and a component amountfor the target component contained in the S second samples.
 4. Anindependent component analysis method in which component calibrationspectra corresponding to a plurality of components contained in eachsample are determined on the basis of a plurality of optical spectraobtained through spectrometry on a plurality of samples, the methodcomprising: (1) extracting a plurality of subsets each including two ormore optical spectra from a set of the plurality of optical spectraobtained through spectrometry on the plurality of samples; and (2)determining a plurality of component calibration spectra respectivelycorresponding to the plurality of components by performing independentcomponent analysis in which component amounts for the plurality ofcomponents in each sample are treated as independent components on eachof the plurality of subsets.